Phase-inverting reactions

VTII. Impact on Molecular Photochemistry and Future Outlook Appendix A Phase Inverting Reactions I. The Model Acknowledgments References... 

We shall assume, for simplifying the notation, that the k values are positive. For a phase-inverting reaction, the wave function of the transition state is therefore written as... 

By using the determinant fomi of the electronic wave functions, it is readily shown that a phase-inverting reaction is one in which an even number of election pairs are exchanged, while in a phase-preserving reaction, an odd number of electron pairs are exchanged. This holds for Htickel-type reactions, and is demonstrated in Appendix A. For a definition of Hilckel and Mbbius-type reactions, see Section III. 

Adopting the view that any theory of aromaticity is also a theory of pericyclic reactions [19], we are now in a position to discuss pericyclic reactions in terms of phase change. Two reaction types are distinguished those that preserve the phase of the total electi onic wave-function - these are phase preserving reactions (p-type), and those in which the phase is inverted - these are phase inverting reactions (i-type). The fomier have an aromatic transition state, and the latter an antiaromatic one. The results of [28] may be applied to these systems. In distinction with the cyclic polyenes, the two basis wave functions need not be equivalent. The wave function of the reactants R) and the products P), respectively, can be used. The electronic wave function of the transition state may be represented by a linear combination of the electronic wave functions of the reactant and the product. Of the two possible combinations, the in-phase one [Eq. (11)] is phase preserving (p-type), while the out-of-phase one [Eq. (12)], is i-type (phase inverting), compare Eqs. (6) and (7). Normalization constants are assumed in both equations ... 

The two coordinates that define the plane in which the loop located were discussed in Section n. In loops that encircle a conical intersection, there is always at least one phase-inverting reaction—we can choose its coordinate as the phase-inverting one. Let us assume that this is the reaction connecting A and... 

A simple VB approach was used in [75] to describe the five structures. Only the lowest energy spin-pairing structures I (B symmehy) of the type (12,34,5 were used (Fig. 21). We consider them as reactant-product pairs and note that the transformation of one structure (e.g., la) to another (e.g., Ib) is a thr ee-electron phase-inverting reaction, with a type-II transition state. As shown in Figure 22, a type-II structure is constructed by an out-of-phase combination of... 

The key to the correct answer is the fact that the conversion of one type-V (or VI) structures to another is a phase-inverting reaction, with a 62 species transition state. This follows from the obseiwation that the two type-V (or VI) stiucture differ by the spin pairing of four electrons. Inspection shows (Fig. 28), that the out-of-phase combination of two A[ structmes is in fact a one,... 

Alternate spin functions (ASF), phase inverting reactions, 498—499 Ammonia molecule ... 

Longuet-Higgins phase-based treatment, three-particle reactive system, 157-168 theoretical background, 43-44 observability, 208 quantum theory, 200 Phase-inverting reactions molecular model, 496-499 phase-change rule, pericyclic reactions, 449-450... 

Cyclooctatetraene (COT) —> Semibullvalene (SB) Photorearrangement. Irradiation of COT yields semibullvalene [97], in spite of the fact that this photochemical reaction is forbidden by orbital conservation mles. The Longuet-Higgins loop for this system actually predicts that this should happen, although the reaction is phase preserving. (Fig. 42). This is another example of type C loop (Fig. 11). Only six of the eight electrons re-pair as COT transforms to SB. The reaction is made possible by the fact that COT valence isomerization, a phase-inverting reaction (four electron-pair Hiickel system), takes place simultaneously. One expects to produce in the reaction a COT isomer, that can be detected solely by proper substitution. 

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